A method for designing the resonant frequency of a dual-frequency machine-dithered laser gyroscope

Abstract

The present invention relates to the field of dual-frequency machine-shaking laser gyroscopes, and specifically to a dual-frequency machine-shaking laser gyroscope resonant frequency design method; based on the simulation results of a virtual simulation model and the vibration test results of the laser gyroscope, a dual-frequency machine-shaking laser gyroscope resonant frequency simulation error model with gyro dynamic stiffness parameters as design variables is established, and the minimization of the errors of each order of resonant frequency is taken as the optimization goal, and through optimization iteration, the first-order resonant frequency of a matching gyroscope consistent with the first-order resonant frequency of a main gyroscope is obtained, forming a final dual-frequency machine-shaking laser gyroscope resonant frequency design scheme; based on the simulation results and the test results, the method of the present invention can quickly find the optimal resonant frequency by changing the geometric parameters of a shaking mechanism, meet the matching requirements of dual-frequency machine-shaking laser gyroscopes of different sizes, and realize the design of the gyroscope resonant frequency, which is of great significance to improving the modeling accuracy and simulation accuracy of an inertial navigation system.

Description

Technical Field

[0001] The present invention relates to the field of dual-frequency mechanical dither laser gyroscopes, and in particular, to a method for designing the resonant frequency of a dual-frequency mechanical dither laser gyroscope. Background Art

[0002] The laser gyroscope based on the Sagnac effect principle is a non-electromechanical medium and high precision inertial sensitive instrument that has been widely used in the field of inertial technology. It has the advantages of stable performance, high precision, long life, wide dynamic range, excellent linearity of proportional factor and stability. It is an ideal sensor for the new generation of high-sensitivity, high-precision and large dynamic range strapdown inertial navigation system (hereinafter referred to as INS).

[0003] In order to deal with the locking problem of laser gyroscopes, a variety of solutions have been proposed, among which the jitter bias frequency control technology is one of the most effective methods. By adding alternating jitter bias frequency, the gyroscope is in the locked state only for a short time, and works outside the lock zone for most of the rest of the time. Even if the input angular rate is very small, the error caused by the locking is greatly reduced because the total time the gyroscope is in the lock zone is short. Therefore, the design quality of the jitter bias frequency control technology directly affects the accuracy and performance of the mechanical jitter laser gyroscope. In the research and design of the laser gyroscope jitter system, the design of the jitter mechanism is the key.

[0004] When the mechanically jittered laser gyro has angular vibrations of the same frequency but different directions on its rotation axis and output axis, although the net direction of the measured input axis remains unchanged (there is no trend item that changes over time as a whole), the gyro will still be sensitive to and output a constant error on the input axis, that is, a coning motion phenomenon occurs. In order to eliminate this error, the laser frequencies on different axes need to be staggered, that is, in order to avoid mechanical coupling, the three vertically mounted gyroscopes used together should be jittered at different resonant frequencies.

[0005] In addition, in the case of high-precision north-seeking while taking into account both volume and weight, laser gyroscopes are usually used in a high-low combination in many occasions. For example, one gyroscope with a resonant optical path side length of 90 mm (referred to as 90 gyroscope) and two gyroscopes with a resonant optical path side length of 70 mm (referred to as 70 gyroscopes) are used in combination. Because the product was finalized earlier, the 90 gyroscope has a solidified frequency of 340 Hz, 380 Hz, and 420 Hz. Ideally, the 70 gyroscope that matches it should also have these three frequencies, that is, the resonant frequencies of laser gyroscopes of different sizes should match each other and remain consistent.

[0006] Therefore, it is necessary to accurately design and select the resonant frequency of mechanical vibration. The existing design of the resonant frequency of dual-frequency mechanical vibration laser gyroscopes mostly relies on experience. After the design is completed, it takes 3-6 months to process and trial-produce. If it does not meet the requirements, it needs to be iterated again, which has the problems of long cycle and low precision. Finite element analysis uses mathematical approximation methods to simulate real physical systems. This method can be applied in the field of dual-frequency mechanical vibration laser gyroscopes to achieve rapid optimization design of resonant structures. Summary of the invention

[0007] In view of the defects in the prior art, the purpose of the present invention is to provide a method for designing the resonant frequency of a dual-frequency machine-shaking laser gyroscope, realize the resonant frequency design of the machine-shaking gyroscope through computer simulation, and optimize and shorten the design cycle of the gyroscope.

[0008] The technical solution adopted by the present invention is: a method for designing the resonant frequency of a dual-frequency machine-shaking laser gyroscope, which is divided into the following steps:

[0009] 1) Conduct a vibration experiment on the laser gyro to obtain the actual resonance frequencies of each order of the laser gyro; the specific process is as follows:

[0010] 1.1) Define the X direction on the horizontal plane as the direction of the line connecting the two anodes of the gyroscope. The Y direction is perpendicular to the X direction. The Z direction, i.e. the vertical direction, is determined according to the right-hand rule.

[0011] 1.2) Conduct frequency sweep vibration tests in horizontal and vertical directions on the dual-frequency machine-shake laser gyro;

[0012] 1.3) After the shaking mechanism works stably, the amplitude-frequency response and actual resonant frequency of the shaking mechanism are measured. In the experiment, a sinusoidal excitation voltage signal with a constant amplitude of Vd=50V is input, and the frequency of the sinusoidal excitation voltage signal is gradually changed from low frequency to high frequency. The change of the shaking amplitude of the shaking mechanism at this time is recorded to obtain the amplitude-frequency response curve of the shaking mechanism. The resonant frequency in the steady state can be obtained through the curve; the swept frequency vibration test is completed according to the swept frequency vibration test specification, and the values ​​of each order of resonant frequency are read and recorded, which are respectively recorded as The subscript n indicates the nth frequency, and the superscript (k) indicates the kth iteration;

[0013] 2) Based on the geometric model of the real laser gyro, finite element modeling and structural modal analysis are performed to obtain the simulated resonance frequencies of each order; the specific process is as follows:

[0014] 2.1) Carry out finite element modeling of the laser gyro and complete modeling and material parameter setting;

[0015] Referring to the geometric dimensions of the real laser gyroscope, the structural model of the gyroscope was established in Solidworks software, and the model was imported into Ansys software. The modal analysis module was selected, and the material parameters of each component of the gyroscope, such as elastic modulus, Poisson's ratio, density, etc., were set in the Engineering Data of the modal analysis module with reference to the materials used in the real laser gyroscope.

[0016] 2.2) Perform working condition setting and modal simulation calculation and solution;

[0017] Enter the modal analysis module, select the corresponding material of each component in Geometry; set the connection relationship between each component in Connections, set the connection mode between the gyro cavity and the shaking mechanism to binding mode, and set the normal stiffness K of the connection between the gyro cavity and the shaking mechanism a , the connection mode between the shaking mechanism and the installation box is set to the preload mode, and the stiffness K of the connection between the shaking mechanism and the installation box is set b , by adjusting these two stiffnesses, the gyroscope resonant frequency can be designed, and the connections at other locations (including the connection between piezoelectric ceramics and spokes, anode and gyroscope body, slotted sheet and gyroscope body, getter cover and gyroscope body, flat sheet and gyroscope body, flat sheet and light-combining prism, flat sheet and frequency-stabilizing prism, grabber and cavity, and adapter resistor and cavity) are made without separation; in Mesh, divide the finite element meshes of the shaking mechanism, mounting box, cavity, anode, slotted sheet, getter cover, frequency-stabilizing prism, adapter resistor, and grabber in the dual-frequency machine-shaking laser gyroscope, and set the mesh size; in Modal, apply boundary conditions, that is, set the bottom surface of the gyroscope mounting box as a fixed support constraint; in Solution, select Total Deformation and click Solve to solve;

[0018] 2.3) After the solution is completed, read the results of each modal order, observe the modal vibration shape, and find the simulated resonance frequencies of each order, which are recorded as The subscript n indicates the nth frequency, and the superscript (k) indicates the kth iteration;

[0019] 3) Compare the simulation results with the experimental results of step 1), establish the simulation error model of each order resonant frequency, and convert the obtained equivalent stiffness K a , K bPass it to Ansys for the next modeling. Change the geometric parameters of the gyroscope, including the thickness of the spokes of the shaking mechanism, the radius of the center hole of the shaking mechanism, the thickness of the piezoelectric ceramic, the length of the piezoelectric ceramic, and the width of the piezoelectric ceramic. Repeat the finite element modeling and structural modal analysis and vibration test of the laser gyroscope for iteration until the final required resonant frequency is obtained, so that the three resonant frequencies of the matching gyroscope (such as the 70 gyroscope) are consistent with the three resonant frequencies of the main gyroscope (such as the 90 gyroscope). The specific process is as follows:

[0020] 3.1) Compare the simulation results with the experimental results of step 1), establish the simulation error model of each order resonant frequency, and convert the obtained equivalent stiffness K a , K b Pass to Ansys for next modeling:

[0021] 3.1.1) Establish the simulation error model of each order resonant frequency. The physical parameters that need to be identified in the laser gyro dynamic stiffness parameters are the normal stiffness K of the connection between the gyro shaking mechanism and the gyro cavity. a and the stiffness K of the connection between the gyro shaking mechanism and the mounting box b The design variable is the gyro equivalent stiffness parameter K that needs to be identified. a , K b :

[0022] ......

[0023]

[0024] Among them, the function represents the equivalent stiffness parameter at the kth iteration Frequency Deviation The complex mapping relationship between them can be solved by using optimization algorithm, so there is no need to know the detailed expression inside the function.

[0025] 3.1.2) The error values ​​of each frequency order are all less than v Hz, 0≤v≤30, which is the constraint function of the error analysis model;

[0026] The objective function is:

[0027]

[0028] The constraints are:

[0029] ......

[0030]

[0031] 3.1.3) According to engineering experience, Ka The initial value is a N / m 3 , 1E6≤a≤1E10,;

[0032] K b The initial value is b N / m 3 , 1E3≤b≤1E7,;

[0033] 3.1.4) Iterative calculation

[0034]

[0035] Will get The values ​​are passed to Ansys for the next modeling.

[0036] 3.2) Set the Solidworks software and Ansys software to be linked, and modify the geometric parameters of the laser gyro in the Solidworks software, including the thickness of the spokes of the shaking mechanism, the radius of the center hole of the shaking mechanism, the thickness of the piezoelectric ceramic, the length of the piezoelectric ceramic, and the width of the piezoelectric ceramic; only modify one parameter at a time: as follows:

[0037] 3.2.1) Fix other parameters and only modify the spoke thickness of the shaking mechanism. Set the spoke thickness range to 0.5mm to 5mm, and increase by 0.5mm each time;

[0038] 3.2.2) Fix other parameters and only modify the radius of the center hole of the shaking mechanism. Set the radius range of the center hole to 20mm to 80mm, and increase it by 5mm each time.

[0039] 3.2.3) Fix other parameters and only modify the thickness of the piezoelectric ceramic of the shaking mechanism. Set the thickness range of the piezoelectric ceramic to 1mm to 10mm, and increase by 1mm each time;

[0040] 3.2.4) Fix other parameters and only modify the length of the piezoelectric ceramic of the shaking mechanism. Set the length range of the piezoelectric ceramic to 50mm to 80mm, and increase by 5mm each time;

[0041] 3.2.5) Fix other parameters and only modify the width of the piezoelectric ceramic of the shaking mechanism. Set the width range of the piezoelectric ceramic to 20mm to 40mm, and increase by 5mm each time;

[0042] 3.3) Select Update Project in the Ansys software to update the project results and obtain the resonance frequencies of each order of the simulation after the parameters are changed.

[0043] 3.4) Modify the geometric parameters of the laser gyro to be the same as the parameters modified in the simulation, repeat step 1), conduct a vibration test of the laser gyro, and obtain the actual resonance frequencies of each order after changing the geometric parameters.

[0044] 3.5) Repeat steps 3.1), 3.2), 3.3), and 3.4) until all parameter settings in 3.2 are traversed.

[0045] 4) A linear regression model is constructed with the geometric parameters traversed multiple times in step 3) as independent variables and the corresponding 1st-order resonance frequency obtained by the vibration test as the dependent variable. Based on the above linear regression model, the geometric parameters corresponding to the required 1st-order resonance frequency (i.e., the resonance frequency of the main gyroscope) are finally found, so that the 1st-order resonance frequency of the matching gyroscope (such as the 70 gyroscope) is consistent with the 1st-order resonance frequency of the main gyroscope (such as the 90 gyroscope).

[0046] The linear regression model is built based on parameter-driven finite element simulation software, and each iteration in the optimization process requires a round of simulation calculations;

[0047] By changing the gyro equivalent stiffness parameter value and the geometric parameters of the laser gyro, after simulation iterations, the equivalent stiffness value that meets the engineering accuracy requirements is finally obtained, so that the first-order resonant frequency of the matching gyro (such as the 70 gyro) is consistent with the first-order resonant frequency of the main gyro (such as the 90 gyro), realizing the design of the resonant frequency of the dual-frequency machine-shake laser gyroscope.

[0048] The present invention is based on the following principles: based on the simulation results of the virtual simulation model and the vibration test results of the laser gyroscope, a dual-frequency machine-shaking laser gyroscope resonant frequency simulation error model is established with the gyroscope equivalent stiffness parameters as design variables, and the minimization of the errors of each order of resonant frequency is taken as the optimization goal. Through optimization iteration, the first-order resonant frequency of the matching gyroscope (such as a 70 gyroscope) that is consistent with the first-order resonant frequency of the main gyroscope (such as a 90 gyroscope) is obtained, forming the final dual-frequency machine-shaking laser gyroscope resonant frequency design scheme.

[0049] The present invention has the following technical effects: based on simulation results and test results, the method of the present invention can quickly find the optimal resonant frequency by changing the gyro equivalent stiffness parameter value and the geometric parameters of the laser gyro, meet the matching requirements of dual-frequency machine-shake laser gyros of different sizes, and realize the design of the gyro resonant frequency; establish an error analysis optimization model, and adopt an optimization algorithm to improve the design efficiency, which is of great significance to improving the modeling accuracy and simulation accuracy of the inertial navigation system. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 :Flowchart of a method for designing the resonant frequency of a dual-frequency machine-dithered laser gyroscope;

[0051] Figure 2: Finite element simulation results of the resonant frequency of the dual-frequency machine-shaking laser gyro;

[0052] Figure 3 : Schematic diagram of the dual-frequency machine-shaking laser gyro frequency-sweep vibration experimental device;

[0053] Figure 4 : Schematic diagram of geometric parameters of laser gyro jitter mechanism. DETAILED DESCRIPTION

[0054] The present invention is further described below.

[0055] Based on the simulation results of the virtual simulation model and the vibration test results of the physical prototype, the present invention establishes a dual-frequency machine-shaking laser gyro resonant frequency simulation error model with the gyro equivalent stiffness parameters as the design variables, takes the minimum error of each order resonant frequency as the optimization goal, and obtains the resonant frequency of the 70 gyro that is consistent with the three resonant frequencies of the 90 gyro through optimization iteration, forming the final dual-frequency machine-shaking laser gyro resonant frequency design scheme. The flowchart of the overall idea is as follows Figure 1 As shown, a dual-frequency machine-shaking laser gyro resonant frequency design method provided by the present invention includes the following steps:

[0056] 1) Conduct a vibration experiment on a 70 gyroscope to obtain the actual resonance frequencies of each order.

[0057] 1.1) Define the horizontal direction as X and Y directions. The X direction is the direction of the line connecting the two anodes of the gyroscope. The Y direction is perpendicular to the X direction. Define the Z direction according to the right-hand rule.

[0058] 1.2) According to the defined coordinate system direction, the 70 gyro is subjected to horizontal and vertical frequency sweep vibration test;

[0059] 1.3) After the shaking mechanism works stably, the amplitude-frequency response and actual resonant frequency of the shaking mechanism are measured. In the experiment, a sinusoidal excitation voltage signal with a constant amplitude of Vd=50V is input. The frequency of the excitation voltage signal is gradually changed from low frequency to high frequency, and the change of the shaking amplitude at this time is recorded to obtain the amplitude-frequency response curve of the shaking mechanism. The resonant frequency in the steady state can be obtained through this curve; the swept frequency vibration test is completed according to the swept frequency vibration test specification, and the values ​​of each order of resonant frequency are read and recorded, which are recorded as The subscript n refers to the nth frequency order, and the superscript (k) refers to the kth iteration.

[0060] 2) Perform finite element modeling and structural modal analysis based on the real 70 gyroscope geometric model to obtain the simulated resonance frequencies of each order.

[0061] 2.1) Carry out finite element modeling of the laser gyro and complete modeling and material parameter setting;

[0062] Referring to the geometric dimensions of the real 70 gyroscope, the structural model of the gyroscope was established in Solidworks software, and the model was imported into Ansys software. The modal analysis module was selected, and the materials used in the real laser gyroscope, including super Invar alloy, microcrystalline glass, 7075-T6, etc., were referred to. In the Engineering Data of the above modules, the material parameters of each component of the gyroscope were set, such as elastic modulus, Poisson's ratio, density, etc. The material parameters can be referred to the document "Inertial Technology Manual / Edited by Yang Lixi. - Beijing: China Aerospace Press, 2013.12".

[0063] 2.2) Perform working condition setting and modal simulation calculation and solution;

[0064] Enter the modal analysis module, select the corresponding material of each component in Geometry; set the connection relationship between each component in Connections, set the connection mode between the gyro cavity and the shaking mechanism to binding mode, and set the normal stiffness K of the connection between the gyro cavity and the shaking mechanism a , the connection mode between the shaking mechanism and the installation box is set to the preload mode, and the stiffness K of the connection between the shaking mechanism and the installation box is set b By adjusting these two stiffnesses, the resonant frequency of the gyroscope can be designed. The connections at other locations (including the connection between the piezoelectric ceramic and the spoke, the anode and the gyroscope body, the slot and the gyroscope body, the getter cover and the gyroscope body, the flat plate and the gyroscope body, the flat plate and the light-combining prism, the flat plate and the frequency-stabilizing prism, the grab and the cavity, and the adapter resistor and the cavity) are made without separation. In Mesh, the finite element meshes of the shaking mechanism, the mounting box, the cavity, the anode, the slot, the getter cover, the frequency-stabilizing prism, the adapter resistor, and the grab in the dual-frequency machine-shaking laser gyroscope are divided, and the mesh size is set. In Modal, boundary conditions are applied, that is, the bottom surface of the gyroscope mounting box is set as a fixed support constraint. In Solution, select Total Deformation and click Solve to solve.

[0065] 2.3) After the simulation results are post-processed, the modal results of each order are read, the modal vibration shapes are observed, and the resonance frequencies of each order of the simulation are found, which are recorded as The subscript n refers to the nth frequency order, and the superscript (k) refers to the kth iteration.

[0066] 3) Compare the simulation results with the experimental results of step 1), establish the simulation error model of each order resonant frequency, and convert the obtained equivalent stiffness K a , K bPass it to Ansys for the next modeling. Change the geometric parameters of the gyroscope, including the thickness of the spokes of the shaking mechanism, the radius of the center hole of the shaking mechanism, the thickness of the piezoelectric ceramic, the length of the piezoelectric ceramic, and the width of the piezoelectric ceramic. Repeat the finite element modeling and structural modal analysis and vibration test of the laser gyroscope for iteration until the final required resonant frequency is obtained, so that the resonant frequency of the 70 gyroscope is consistent with the resonant frequency of the 90 gyroscope, 380Hz. The specific process is as follows;

[0067] 3.1) Based on the experimental and simulation results, an error analysis and optimization model is established, and the gyro equivalent stiffness parameters are optimized using an optimization algorithm. The specific process is as follows:

[0068] 3.1.1) Establish the simulation error model of each order resonant frequency. The physical parameters that need to be identified in the laser gyro dynamic stiffness parameters are the normal stiffness K of the connection between the gyro shaking mechanism and the gyro cavity. a and the stiffness K of the connection between the gyro shaking mechanism and the mounting box b The design variable is the gyro equivalent stiffness parameter K that needs to be identified. a , K b :

[0069] ......

[0070]

[0071] Among them, the function Represents the equivalent stiffness parameter Frequency Deviation The subscript n represents the nth order frequency, and the superscript (k) represents the kth iteration. Since the optimization algorithm is used for solving, there is no need to know the detailed expression inside the function.

[0072] 3.1.2) The error values ​​of each frequency order are all less than 5 Hz, which is the constraint function of the error analysis model;

[0073] The objective function is:

[0074]

[0075] The constraints are:

[0076] ......

[0077]

[0078] 3.1.3) According to engineering experience, K a The initial value is 1E7 N / m 3 ;

[0079] K b The initial value is 1E4 N / m 3 ;

[0080] 3.1.4) Iterative calculation

[0081]

[0082] Will get The values ​​are passed to Ansys for the next modeling.

[0083] 3.2) Set the Solidworks software and Ansys software to be linked, and modify the geometric parameters of the laser gyro in the Solidworks software, including the thickness of the spokes of the shaking mechanism, the radius of the center hole of the shaking mechanism, the thickness of the piezoelectric ceramic, the length of the piezoelectric ceramic, and the width of the piezoelectric ceramic. Only one parameter is modified at a time; the details are as follows:

[0084] 3.2.1) Fix other parameters and only modify the spoke thickness of the shaking mechanism. Set the spoke thickness range to 0.5mm to 5mm, and increase by 0.5mm each time;

[0085] 3.2.2) Fix other parameters and only modify the radius of the center hole of the shaking mechanism. Set the radius range of the center hole to 20mm to 80mm, and increase it by 5mm each time.

[0086] 3.2.3) Fix other parameters and only modify the thickness of the piezoelectric ceramic of the shaking mechanism. Set the thickness range of the piezoelectric ceramic to 1mm to 10mm, and increase by 1mm each time;

[0087] 3.2.4) Fix other parameters and only modify the length of the piezoelectric ceramic of the shaking mechanism. Set the length range of the piezoelectric ceramic to 50mm to 80mm, and increase by 5mm each time;

[0088] 3.2.5) Fix other parameters and only modify the width of the piezoelectric ceramic of the shaking mechanism. Set the width range of the piezoelectric ceramic to 20mm to 40mm, and increase by 5mm each time;

[0089] 3.3) Select Update Project in the Ansys software to update the project results and obtain the resonance frequencies of each order of the simulation after the parameters are changed.

[0090] 3.4) Modify the geometric parameters of the laser gyro to be the same as the parameters modified in the simulation, repeat step 1), conduct a vibration test of the laser gyro, and obtain the actual resonance frequencies of each order after changing the geometric parameters.

[0091] 3.5) Repeat steps 3.1), 3.2), 3.3), and 3.4) until all parameter settings in 3.2 are traversed.

[0092] 4) A linear regression model is constructed with the geometric parameters traversed multiple times in step 3) as independent variables and the corresponding 1st-order resonant frequency obtained by the vibration test as the dependent variable. Based on the above linear regression model, the geometric parameters corresponding to the required 1st-order resonant frequency (i.e., the resonant frequency of the main gyroscope) are finally found, so that the 1st-order resonant frequency of the 70 gyroscope is consistent with the 1st-order resonant frequency of the 90 gyroscope, 380 Hz.

[0093] The linear regression model is built based on parameter-driven finite element simulation software, and each iteration in the optimization process requires a round of simulation calculations;

[0094] By changing the gyro equivalent stiffness parameter value and through simulation iterations, the equivalent stiffness value that meets the engineering precision requirements is finally obtained, so that the three resonant frequencies of the matching gyro (70 gyro) are consistent with the three resonant frequencies of the main gyro (90 gyro), realizing the design of the resonant frequency of the dual-frequency machine-shake laser gyroscope.

[0095] In summary, the present invention solves the problems of low precision, reliance on experience, and difficulty in rapid optimization in the existing dual-frequency machine-shaking laser gyro resonant frequency design, solves the problem of frequency consistency, improves the compatibility of the gyro, and facilitates the replacement and design of the gyro. At the same time, the present invention realizes the precise design of the resonant frequency through finite element analysis and optimization iteration methods, improves the design efficiency and effect, and is suitable for the design of laser gyro systems with complex structures.

Claims

1. A method for designing the resonant frequency of a dual-frequency machine-shaking laser gyroscope, characterized in that: The method is divided into the following steps: 1) Conduct a vibration experiment on the laser gyro to obtain the actual resonance frequencies of each order of the laser gyro; the specific process is as follows: 1.1) Define the X direction on the horizontal plane as the direction of the line connecting the two anodes of the gyroscope, the Y direction is perpendicular to the X direction, and the Z direction, i.e. the vertical direction, is determined according to the right-hand rule; 1.2) Conduct frequency sweep vibration tests in horizontal and vertical directions on the dual-frequency machine-shake laser gyro; 1.3) After the shaking mechanism works stably, the amplitude-frequency response and actual resonant frequency of the shaking mechanism are measured. In the experiment, a sinusoidal excitation voltage signal with a constant amplitude of Vd=50V is input, and the frequency of the sinusoidal excitation voltage signal is gradually changed from low frequency to high frequency. The change of the shaking amplitude of the shaking mechanism at this time is recorded to obtain the amplitude-frequency response curve of the shaking mechanism. The resonant frequency in the steady state can be obtained through this curve; the swept frequency vibration test is completed according to the swept frequency vibration test specification, and the values ​​of each order of resonant frequency are read and recorded, which are respectively recorded as F1 (k) , The subscript n indicates the nth frequency, and the superscript (k) indicates the kth iteration; 2) Based on the geometric model of the real laser gyro, finite element modeling and structural modal analysis are performed to obtain the simulated resonance frequencies of each order; the specific process is as follows: 2.1) Carry out finite element modeling of the laser gyro and complete modeling and material parameter setting; Referring to the geometric dimensions of the real laser gyro, the structural model of the gyro was established in Solidworks software, and the model was imported into Ansys software. The modal analysis module was selected, and the elastic modulus, Poisson's ratio, and density of each component of the gyro were set in the Engineering Data of the modal analysis module with reference to the materials used in the real laser gyro. 2.2) Perform working condition setting and modal simulation calculation and solution; Enter the modal analysis module, select the corresponding material of each component in Geometry; set the connection relationship between each component in Connections, set the connection mode between the gyro cavity and the shaking mechanism to binding mode, and set the normal stiffness K of the connection between the gyro cavity and the shaking mechanism a , the connection mode between the shaking mechanism and the installation box is set to the preload mode, and the stiffness K of the connection between the shaking mechanism and the installation box is set b By adjusting these two stiffnesses, the gyroscope resonant frequency can be designed. The connections at other places, including the connection between piezoelectric ceramics and spokes, anode and gyroscope body, slotted sheet and gyroscope body, getter cover and gyroscope body, flat sheet and gyroscope body, flat sheet and light-combining prism, flat sheet and frequency-stabilizing prism, grabber and cavity, and adapter resistor and cavity, adopt a non-separation method; divide the finite element mesh of the shaking mechanism, mounting box, cavity, anode, slotted sheet, getter cover, frequency-stabilizing prism, adapter resistor, and grabber in the dual-frequency machine-shaking laser gyroscope in Mesh, and set the mesh size; apply boundary conditions in Modal, that is, set the bottom surface of the gyroscope mounting box as a fixed support constraint; select Total Deformation in Solution, and click Solve to solve; 2.3) After the solution is completed, read the results of each modal order, observe the modal vibration shape, and find the simulated resonance frequency of each order, which are recorded as f1 and f2. (k) , The subscript n indicates the nth frequency, and the superscript (k) indicates the kth iteration; 3) Compare the simulation results with the experimental results of step 1), establish the simulation error model of each order resonant frequency, and convert the obtained equivalent stiffness K a , K b Transfer to Ansys for the next modeling; change the geometric parameters of the gyroscope, including the thickness of the spokes of the shaking mechanism, the radius of the center hole of the shaking mechanism, the thickness of the piezoelectric ceramic, the length of the piezoelectric ceramic, and the width of the piezoelectric ceramic. Repeat the finite element modeling and structural modal analysis and vibration test of the laser gyroscope for iteration until the final required resonant frequency is obtained, so that the three resonant frequencies of the matching gyroscope are consistent with the three resonant frequencies of the main gyroscope. The specific process is as follows: 3.1) Compare the simulation results with the experimental results of step 1), establish the simulation error model of each order resonant frequency, and convert the obtained equivalent stiffness K a , K b Pass to Ansys for next modeling: 3.1.1) Establish the simulation error model of each order resonant frequency; the physical parameters that need to be identified in the laser gyro dynamic stiffness parameters are the normal stiffness K of the connection between the gyro shaking mechanism and the gyro cavity a and the stiffness K of the connection between the gyro shaking mechanism and the mounting box b : Among them, the function represents the equivalent stiffness parameter at the kth iteration Frequency Deviation The complex mapping relationship between them can be solved by using optimization algorithms, so there is no need to know the detailed expressions inside the functions. 3.1.2) The error values ​​of each frequency order are all less than v Hz, which is the constraint function of the error analysis model; The objective function is: The constraints are: 3.1.3) According to engineering experience, K a The initial value is a N / m 3 ; K b The initial value is b N / m 3 ; 3.1.4) Iterative calculation Will get The value is passed to Ansys for the next modeling; 3.2) Set the Solidworks software and Ansys software to be linked, and modify the geometric parameters of the laser gyro in the Solidworks software, including the thickness of the spokes of the shaking mechanism, the radius of the center hole of the shaking mechanism, the thickness of the piezoelectric ceramic, the length of the piezoelectric ceramic, and the width of the piezoelectric ceramic; only modify one parameter at a time: as follows: 3.2.1) Fix other parameters and only modify the spoke thickness of the shaking mechanism. Set the spoke thickness range to 0.5mm to 5mm, and increase by 0.5mm each time; 3.2.2) Fix other parameters and only modify the radius of the center hole of the shaking mechanism. Set the radius range of the center hole to 20mm to 80mm, and increase it by 5mm each time. 3.2.3) Fix other parameters and only modify the thickness of the piezoelectric ceramic of the shaking mechanism. Set the thickness range of the piezoelectric ceramic to 1mm to 10mm, and increase by 1mm each time; 3.2.4) Fix other parameters and only modify the length of the piezoelectric ceramic of the shaking mechanism. Set the length range of the piezoelectric ceramic to 50mm to 80mm, and increase by 5mm each time; 3.2.5) Fix other parameters and only modify the width of the piezoelectric ceramic of the shaking mechanism. Set the width range of the piezoelectric ceramic to 20mm to 40mm, and increase by 5mm each time; 3.3) Select Update Project in Ansys software to update the project results and obtain the resonance frequencies of each order of the simulation after the parameters are changed; 3.4) Modify the geometric parameters of the laser gyro to be the same as the parameters modified in the simulation, repeat step 1), conduct a vibration test of the laser gyro, and obtain the actual resonance frequencies of each order after changing the geometric parameters; 3.5) Repeat steps 3.1), 3.2), 3.3), and 3.4) until all parameter settings in 3.2 are traversed; 4) A linear regression model is constructed with the geometric parameters traversed multiple times in step 3) as independent variables and the first-order resonance frequency obtained by the corresponding vibration test as the dependent variable; based on the above linear regression model, the geometric parameters corresponding to the required first-order resonance frequency are finally found, so that the first-order resonance frequency of the matching gyroscope is consistent with the first-order resonance frequency of the main gyroscope; The linear regression model is built based on parameter-driven finite element simulation software, and each iteration in the optimization process requires a round of simulation calculations to be completed; By changing the gyro equivalent stiffness parameter value and the geometric parameters of the laser gyro, after simulation iterations, the equivalent stiffness value that meets the engineering accuracy requirements is finally obtained, so that the first-order resonant frequency of the mating gyro is consistent with the first-order resonant frequency of the main gyro, realizing the design of the resonant frequency of the dual-frequency machine-shake laser gyroscope.

2. A method for designing the resonant frequency of a dual-frequency machine-shaking laser gyro according to claim 1, characterized in that: The cooperating gyro is a 70 gyro and the main gyro is a 90 gyro.

3. A method for designing the resonant frequency of a dual-frequency machine-shaking laser gyro according to claim 1, characterized in that: In 3.1.2, the error values ​​of each frequency order are less than v Hz, 0≤v≤30.

4. A method for designing the resonant frequency of a dual-frequency machine-shaking laser gyro according to claim 3, characterized in that: v=5Hz.

5. A method for designing the resonant frequency of a dual-frequency machine-dithered laser gyro according to claim 1, characterized in that: In 3.1.3, K a The initial value satisfies 1E6≤a≤1E10, K b The initial value satisfies 1E3≤b≤1E7.

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